Hole Diameter and Sinking Time of Water Clocks

摘要

Water clocks measure time by controlling the flow of water intoa container. Ancient Persians used the sinking time of Fenjaans,bowls with holes in the center,as a metric for time. The relationship between hole diameter and sinking time of cylindrical containerswas investigated. Atheoretical model was derived using Torricelli’s Law and Archimedes’ Principle. The experimentalrelationship was found by drillingholes with diameters ranging from 2 to 13mm inthe center of nearly cylindrical stainless-steel containersand measuring their sinking time. It was found that there was a proportional relationship between the sinking time and the inverse square of thehole diameter with a proportionality constant which matched, within uncertainties, the proportionality constant predicted bythe theoretical model.